Question

A base of a parallelogram is on the x-axis and the origin is located at the left endpoint of that base. Three consecutive vertices are (h, j), (0, 0), and (k, 0), where h > 0.

What is the y- coordinate of the fourth vertex?
h
j
k

Answer 1

j

Explanation:

Answer 2

The y-coordinate of the fourth vertex is j.

Explanation:

Since, the diagonals of parallelogram bisect each othe,

That is, the midpoint of one diagonal = the midpoint of the other diagonal,

Here, the consecutive vertices are (h, j), (0, 0), and (k, 0), where h > 0,

Let (x,y) are the coordinates of fourth vertex,

⇒ Midpoint of coordinates (h, j) and (k, 0) = Midpoint of coordinate (0,0) and (x,y)

`\implies ((h+k)/(2), (j+0)/(2))=((0+x)/(2),(0+y)/(2))`

By comparing the y-coordinates,

`(j+0)/(2)=(0+y)/(2)`

`\implies y=j`

Hence, the y-coordinate of the fourth vertex is j.

Second option is correct.